PSI - Issue 52

Satrio Wicaksono et al. / Procedia Structural Integrity 52 (2024) 438–454

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Satrio Wicaksono et al. / Structural Integrity Procedia 00 (2023) 000 – 000

where p

: Pressure stress : Mises stress : Deviatoric stress

q S B α

: The size of the q axis (vertical) of the yield ellipse

: The shape factor of the yield ellipse which defines the relative size from the axis

: Yield stress in hydrodynamic compression

p c σ c

: The absolute value of the yield stress in uniaxial compression The yield surface represents the Mises circle in the deviatoric stress plane. The shape factor, α, can be calculated using the initial yield stress in uniaxial compression, 0 , and the initial yield stress in hydrostatic compression, 0 , with: = 3 √9− 2 , ℎ = 0 0 =√3(1 − 2( )) , ℎ = ′ To determine the shape of the ellipse, the value of k is needed. For a valid yield surface, the strength ratio must be such that 0 ≤ k < 3. The particular case of k = 0 corresponds to Mises plasticity. In general, the initial yield stresses in uniaxial compression and in hydrostatic compression, 0 and 0 , can be used to calculate the value of k. However, in many practical cases, the stress-strain response curve of crushable foam materials does not show a clear yielding point, and the initial yield stress value cannot be determined precisely. Many of these response curves have horizontal plateaus or nearly constant yield stresses over a very large range of plastic strain values. b. Hardening A simple uniaxial compression test is sufficient to determine the evolution of the yield surface. The hardening law defines the value of the yield stress in uniaxial compression as a function of the absolute value of the axial plastic strain. c. Rate Dependence As the strain rate increases, many materials show an increase in yield stress. For many crushable foam materials, this increase in yield stress becomes important when the strain rate is in the range of 0.1 – 1 per second and can be especially important when the strain rate is in the range of 10 – 100 per second, as is common in high-density events. dynamic energy. 2.1.3. Ductile damage This model is one of the most commonly used damage initiation criterions for capturing damage in ductile materials. Unlike other damage model that use stress as initiation criterion, in this model plastic strain was used instead. In this study, the ductile damage was used to model the damage initiation for both foam and aluminum materials [15]. The ductile failure criterion model [16] assumes that the plastic strain at the onset of damage, , is a function of the triaxiality of the stress and the strain rate with the equation: ( , ̇ ) where η : stress triaxiality, η = − P/q P : pressure stress